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The current pandemic, caused by the outbreak of a novel coronavirus (COVID-19) in December 2019, has led to a global emergency that has significantly impacted economies, healthcare systems and personal wellbeing all around the world. Controlling the rapidly evolving disease requires highly sensitive and specific diagnostics. While real-time RT-PCR is the most commonly used, these can take up to 8 hours, and require significant effort from healthcare professionals. As such, there is a critical need for a quick and automatic diagnostic system. Diagnosis from chest CT images is a promising direction. However, current studies are limited by the lack of sufficient training samples, as acquiring annotated CT images is time-consuming. To this end, we propose a new deep learning algorithm for the automated diagnosis of COVID-19, which only requires a few samples for training. Specifically, we use contrastive learning to train an encoder which can capture expressive feature representations on large and publicly available lung datasets and adopt the prototypical network for classification. We validate the efficacy of the proposed model in comparison with other competing methods on two publicly available and annotated COVID-19 CT datasets. Our results demonstrate the superior performance of our model for the accurate diagnosis of COVID-19 based on chest CT images.